A Stochastic Harvest Leslie Matrix Simulation Model For Evaluating Wildlife Population Reconstruction Methods Using Harvest Data

Population reconstruction models are commonly used by wildlife managers to analyze animal populations, although realistic and accurate population information is gener- ally unavailable for evaluating these methods. To aid in the evaluation of population reconstruction models, we developed a stochastic harvest Leslie matrix simulation model that generates population and harvest data. The ergodic results of the pro- jection by the stochastic harvest Leslie matrix simulation model and the stochastic growth rate under such a projection were studied. The stochastic harvest Leslie ma- trix simulation model was proved to generate at least weakly-ergodic population pro- jection results. Through extensive simulation studies, the population age distribution generated by the simulation model was shown to be convergent, which is the usual model assumption underlying population reconstruction methods. A new modeling approach for analyzing population age distribution based only on harvest data was also proposed. Through extensive simulation studies, this new modeling approach was shown to provide accurate estimation of the population age distribution while imposing no strict assumptions on the fertility and the natural mortality of animals. A new R package, Wildlife 1.0, contains the main results from this thesis.

This books presents some of the most recent and advanced statistical methods used to analyse environmental and climate data, and addresses the spatial and spatio-temporal dimensions of the phenomena studied, the multivariate complexity of the data, and the necessity of considering uncertainty sources and propagation. The topics covered include: detecting disease clusters, analysing harvest data, change point detection in ground-level ozone concentration, modelling atmospheric aerosol profiles, predicting wind speed, precipitation prediction and analysing spatial cylindrical data. The volume presents revised versions of selected contributions submitted at the joint TIES-GRASPA 2017 Conference on Climate and Environment, which was held at the University of Bergamo, Italy. As it is chiefly intended for researchers working at the forefront of statistical research in environmental applications, readers should be familiar with the basic methods for analysing spatial and spatio-temporal data.

Age-at-harvest data are routinely collected as part of game-management programs. These data represent a wealth of information regarding demographic processes and trends in wildlife abundance. Use of wildlife age-at-harvest data has blossomed only relatively recently in the literature despite its frequent collection by game management agencies. Statistical models exist for such data, but are limited in their facility, owing to restrictive assumptions regarding constancy of demographic processes, unsuitability of models for the type of data collected, or computing difficulty in fitting models. Current models cannot accommodate the presence of process error (natural variation in demographic processes), or separate this error from sampling error (measurement error that is present whenever the full population cannot be sampled). I develop and examine a set of statistical models for demographic processes using primarily age-at-harvest data that can be used to estimate survival probability, harvest vulnerability, and recruitment, as well as process error associated with these entities. I conduct thorough simulation studies of these models, and assess them with respect to their ability to accurately and precisely reconstruct abundance. Studies are conducted for fully-aged big game harvest, pooled age-class big-game harvest, and small-game harvest. Results indicate that a mixed-effects model which incorporates random effects in the processes of natural mortality and harvest probability, as well as a likelihood conditional on total cohort capture along with a Horvitz-Thompson abundance estimator outperform other models, and are recommended for use.

Historically, management agencies in the United States have monitored most game populations through an ad hoc approach which combines indices, harvest data, hunter surveyed data, and occasional demographic evaluation. However, changing management priorities and increased scrutiny require more informative and defensible means of monitoring harvested populations. Statistical population reconstruction (SPR) is a flexible modeling system which simultaneously analyzes age-at-harvest data, hunter effort data and any additional demographic data which are available, producing estimates of abundance, natural survival and harvest rate, as well as their associated variances. An SPR based monitoring framework provides comprehensive analysis of commonly collected data and represents a statistically rigorous and defensible alternative to the currently popular approaches. However, applications of SPR have previously been limited to small scale, highly monitored populations, primarily due to a lack of formal evaluation of data requirements and guidance for management application. In this dissertation I provide the guidance necessary for broad scale application of SPR modeling to monitor harvested species. I rigorously evaluate the relative utility of auxiliary data sources as well as minimum harvest and hunter effort data requirements for SPR models, providing necessary guidance for resource managers seeking to apply SPR. I present a historic population reconstruction based on SPR parameter estimates as an illustrative example of the management application potential of SPR output. I comprehensively evaluate models to project reconstructed abundance into the future in order to further increase the management utility of statistical population reconstruction. I provide a detailed explanation of model structure and assumptions, allowing resource managers to critically evaluate SPR models. Finally, I offer guidance on the customization of SPR models necessary to adequately model the harvest regimes and data collection methodologies which are unique to each harvested population, thus increasing the number of populations which can be modeled. This dissertation will facilitate the broad scale management application of SPR, thus increasing the rigor and efficiency with which harvested game populations are monitored.

This comprehensive book, rich with applications, offers a quantitative framework for the analysis of the various capture-recapture models for open animal populations, while also addressing associated computational methods. The state of our wildlife populations provides a litmus test for the state of our environment, especially in light of global warming and the increasing pollution of our land, seas, and air. In addition to monitoring our food resources such as fisheries, we need to protect endangered species from the effects of human activities (e.g. rhinos, whales, or encroachments on the habitat of orangutans). Pests must be be controlled, whether insects or viruses, and we need to cope with growing feral populations such as opossums, rabbits, and pigs. Accordingly, we need to obtain information about a given population’s dynamics, concerning e.g. mortality, birth, growth, breeding, sex, and migration, and determine whether the respective population is increasing , static, or declining. There are many methods for obtaining population information, but the most useful (and most work-intensive) is generically known as “capture-recapture,” where we mark or tag a representative sample of individuals from the population and follow that sample over time using recaptures, resightings, or dead recoveries. Marks can be natural, such as stripes, fin profiles, and even DNA; or artificial, such as spots on insects. Attached tags can, for example, be simple bands or streamers, or more sophisticated variants such as radio and sonic transmitters. To estimate population parameters, sophisticated and complex mathematical models have been devised on the basis of recapture information and computer packages. This book addresses the analysis of such models. It is primarily intended for ecologists and wildlife managers who wish to apply the methods to the types of problems discussed above, though it will also benefit researchers and graduate students in ecology. Familiarity with basic statistical concepts is essential.

The problem of estimating animal abundance is common in wildlife management and environmental impact assessment. Capture-recapture and removal methods are often used to estimate population size. Statistical Inference From Capture Data On Closed Animal Populations, a monograph by Otis et al. (1978), provides us with a comprehensive synthesis of much of the wildlife and statistical literature on the methods, as well as some extensions of the general theory. In our primer, we focus on capture-recapture and removal methods for trapping studies in which a population is assumed to be closed and do not treat open-population models, such as the Jolly-Seber model, or catch-effort methods in any detail. The primer, written for students interested in population estimation, is intended for use with the more theoretical monograph.